A large spectrum of new technologies are being explored in the optical disk drive systems. Optics, lasers, media, and servomechanisms are a few examples. This thesis will be directed to the study of a servomechanism used in a majority of the optical disk drives, commonly referred to as the tracking servomechanism. The tracking servomechanism, consisting of a fine and a coarse actuator, is mechanically analyzed by the use of free body diagrams. A transfer function for each actuator is derived. Analog compensators are designed to achieve specific phase and gain margin requirements. A digital compensator is derived from the analog compensator by the use of a mapping technique. Major contributions of this thesis include studies to determine an acceptable sampling rate, number of bits, and computation delay associated with the implementation of a digital servo controller in a tracking servomechanism.